1. Field of the Invention
The present invention concerns a method to select an undersampling scheme for sampling k-space and an associated set of reconstruction kernels. Furthermore, the invention concerns a method for magnetic resonance imaging. The present invention furthermore concerns a magnetic resonance system for implementing such a method.
2. Description of the Prior Art
Magnetic resonance (MR) tomography (MRT) is an imaging method that enables the acquisition of two-dimensional or three-dimensional image data sets that can map structures inside an examined person (even soft tissues) with high resolution. In MRT, the magnetic moments of protons in an examination subject are aligned in a basic magnetic field. By radiating radio-frequency pulses, the nuclear spins can be deflected or excited out of the aligned state (i.e. the rest state) or another state. The temporal evolution of the excited magnetization is subsequently detected by one or more radio-frequency (RF) coils.
By applying a slice selection gradient in the radiation of radio-frequency pulses, only nuclear spins in a slice of the examination subject in which the resonance condition is satisfied due to the local magnetic field strength are excited. An additional spatial coding can take place by the application of at least one phase coding gradient as well as a frequency coding gradient during the readout. It is thereby possible to acquire MR exposures of multiple slices of an examined person. By means of suitable presentation methods it is possible to provide a 3-dimensional (3D) image of a defined region of the examined person for diagnosis.
The acquired MR signals are initially present in a spatial frequency domain (also known as k-space) and can be transformed into the image domain by subsequent Fourier transformation. K-space can be scanned (meaning raw (acquired) data are entered into k-space at respective locations therein) with various trajectories by an appropriately designed switching of the magnetic field gradients. A conventional scanning includes the successive acquisition of frequency-coded k-space lines (which are generally oriented along the x-axis of k-space) for respectively different phase codings (that define the y-axis and z-axis of k-space).
Ever faster MR acquisitions—in particular 3D MR acquisitions—are sought in clinical environments. MR measurement sequences to generate MR exposures can be optimized in this regard. For this purpose, 3-dimensional k-space is typically undersampled in two directions, and the missing information is filled in by the use of correlations between signals.
Various different undersamplings are possible, with each measurement being implemented simultaneously with multiple radio-frequency coils. The simultaneously acquired data can be spatially separated by means of suitable computation operations with the knowledge of the spatial acquisition characteristics of the various radio-frequency coils. It is thereby possible to obtain the spatial resolution from the information about the sensitivity of the coils, instead of implementing a relatively slower switching of slice selection gradients. An acceleration factor is defined using the RF coils that are present can be used for parallel imaging. For example, such methods are known under the names “Generalized Auto-Calibrating Partial Parallel Acquisition” (GRAPPA), “Sensitivity Encoding” (SENSE), “Simultaneous Acquisition of Spatial Harmonics” (SMASH) and “Controlled Aliasing in Parallel Imaging Results in Higher Acceleration” (CAIPIRINHA).
In some of these methods, an additional acceleration of the MR imaging can take place by not all points of k-space being scanned. This means that the measurement resolution is decreased in a targeted manner during the data acquisition, in comparison to a maximum achievable measurement resolution. An undersampling of k-space thus occurs. A reduced MR data set thus can be achieved. A reduction factor can characterize the undersampling. If the reduction factor is four, for example, the measurement point density in k-space is reduced by a factor of four. There are various possibilities to implement the undersampling of k-space at a given reduction factor. The manner in which the undersampling takes place is designated as an undersampling scheme. For example, an undersampling scheme can establish which data points are acquired and in what order the data points are acquired, i.e. the trajectory of the data acquisition. Before the assembly of the data of the various coils, the reduced MR data set can be reconstructed so that a reconstructed MR data set is obtained. The reconstruction takes place by the application of a reconstruction kernel to the reduced MR data of each coil. The associated reconstruction kernels of the various coils are designated as a set of reconstruction kernels.
It is possible to associate various reconstruction kernels—that respectively allow the reduced MR data sets to be reconstructed—with an undersampling scheme. From the reconstructed MR image data of the various RF coils it is then possible to calculate a composite MR image in the form of accelerated MR image data.
In CAIPIRINHA and GRAPPA, various possibilities to undersample k-space are known from F. A. Breuer et al., Mag. Res. in Med. 55 (2006), 549. In particular, for a given reduction factor there are multiple possibilities to undersample k-space, i.e. various undersampling schemes. However, it is known that MR images reconstructed from the different undersampling schemes can have different noise. In Breuer et al, a quantification of the signal noise of the image (i.e. of the image noise) takes place using the accelerated and composite image data themselves in the form of a spatially averaged geometry factor (g-factor). However, to select the optimal undersampling scheme this requires first that the complete measurement sequences or computation operations must be implemented for image reconstruction, and then that a quantification of the image noise is implemented using the image data themselves.